If the minimill is anything like the VF3 which I am familiar with, the coolant jacket surrounds the spindle cartridge, so there is a fair reservoir of coolant left in there and gravity will pull it down and out. Perhaps if one wished, you could plumb an additional loop of pipe onto the outlet, run it up to the top of the head and back down again, adding some kind of vacuum breaker valve at the top of the loop to stop siphoning, if necessary. It might not siphon for very long anyway without that detail.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)